Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Numerical analysis of a quasistatic viscoplastic contact problem with friction and damage

M. Campoa,*, J.R. Fernándeza, T.-V. Hoarau-Mantelb
aDepartmento de Matemática Aplicada, Facultade de Matemáticas, Universidade de Santiago de Compostela, Campus Sur, 15782, Santiago de Compostela, Spain bLaboratoire de Théorie des Systèmes, Université de Perpignan, 52 Avenue de Villeneuve, 66860 Perpignan, France

  Full Text
In this paper, a frictional viscoplastic contact problem is studied. The damage, caused by excessive stress or strain is also included and it is modelled by a parabolic differential inclusion. The variational formulation for this problem is obtained and the existence of a unique solution is proved. Then, fully discrete approximations are introduced based on the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived and, under suitable regularity assumptions, the linear convergence of the algorithm is derived. Finally, a numerical test is provided.

Keywords:  Viscoplasticity; Friction; Error estimates; Numerical simulations

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